The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  2  1  1  1  1  X  1  1  0  1  1  X  1  1  X  0  1  1  1 X^2  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X X^2 X^2+X  0 X^2+X  2 X+2 X^2 X^2+X  X  X  0 X^2+X X^2+2 X+2  2 X^2+X+2  0  X X^2 X+2 X^2+X+2  0 X+2  X  0 X+2 X^2+X+2 X^2+X  X  2 X^2+X+2
 0  0 X^2+2  0 X^2 X^2  2 X^2 X^2  0  2 X^2+2 X^2 X^2  2  0  2 X^2+2  0  0  2  2 X^2+2 X^2 X^2+2  0 X^2+2 X^2+2 X^2+2  2 X^2+2 X^2 X^2 X^2+2  0  2 X^2  2 X^2
 0  0  0  2  0  0  2  2  2  0  2  2  2  0  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  0  0  0  2  0  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  2  0  0  2

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+112x^35+115x^36+326x^37+289x^38+454x^39+271x^40+268x^41+52x^42+92x^43+29x^44+14x^45+9x^46+14x^47+1x^54+1x^62

The gray image is a code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 2.5 seconds.